The Advanced Technology Solar Telescope (ATST) is a 4-m class solar telescope to be built in Haleakala Observatory in Maui (HI). It will be the largest solar telescope in the world, with unprecedented abilities to view details of the Sun. Using adaptive optics technology, ATST will be able to provide the sharpest views ever taken of the solar surface. It is expected that the 4-meter class telescope will have a significant impact on the study of stellar magnetic fields, plasma physics and astronomy, allowing scientists to learn even more about the Sun and solar-terrestrial interactions. Apart from the traditional weather protection functions, ATST Enclosure supports the telescope Aperture Stop which must be accurately positioned to fully illuminate the primary mirror, while preventing insolation of any other system components. This positioning is performed by the enclosure shutter (altitude) and azimuth mechanisms. In order to evaluate the positioning capabilities of both mechanisms and verify the structure-mechanism-control interaction of the involved systems a dynamic coupled model has been created. On the other hand, the skin of the enclosure is thermally controlled to avoid the ''enclosure seeing'' by rejecting solar radiation and keeping its surface temperature as close as possible below the ambient temperature. The thermal control is achieved by a set of water cooled plate coils. The cooling fluid flow is controlled to achieve the desired reference temperature. The performance of the system is being analyzed by means of mathematical model with couples the thermal radiation analysis and the control system performances.